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Diskr. Mat., 2017, Volume 29, Issue 3, Pages 3–23 (Mi dm1436)  

This article is cited in 5 scientific papers (total in 5 papers)

On the structure of digraphs of polynomial transformations over finite commutative rings with unity

V. E. Viktorenkov


Abstract: The paper describes structural characteristics of the digraph of an arbitrary polynomial transformation of a finite commutative ring with unity. A classification of vertices of the digraph is proposed: cyclic elements, initial elements, and branch points are described. Quantitative results on such objects and heights of vertices are given. Besides, polynomial transformations are shown to have cycles whose lengths coincide with the lengths of cycles of the induced polynomial transformation over the field $R/\Re$, where $\Re$ is the radical of the finite commutative local ring $R$.

Keywords: digraph, polynomial transformation, finite commutative ring.

DOI: https://doi.org/10.4213/dm1436

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English version:
Discrete Mathematics and Applications, 2018, 28:3, 259–274

Bibliographic databases:

UDC: 519.172.3+519.113.6
Received: 25.05.2017

Citation: V. E. Viktorenkov, “On the structure of digraphs of polynomial transformations over finite commutative rings with unity”, Diskr. Mat., 29:3 (2017), 3–23; Discrete Math. Appl., 28:3 (2018), 259–274

Citation in format AMSBIB
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\by V.~E.~Viktorenkov
\paper On the structure of digraphs of polynomial transformations over finite commutative rings with unity
\jour Diskr. Mat.
\yr 2017
\vol 29
\issue 3
\pages 3--23
\mathnet{http://mi.mathnet.ru/dm1436}
\crossref{https://doi.org/10.4213/dm1436}
\elib{http://elibrary.ru/item.asp?id=29887798}
\transl
\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 3
\pages 259--274
\crossref{https://doi.org/10.1515/dma-2018-0023}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85053133300}


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  • https://doi.org/10.4213/dm1436
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. A. Kozlitin, “Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring”, Discrete Math. Appl., 28:6 (2018), 345–358  mathnet  crossref  crossref  isi  elib
    2. O. A. Kozlitin, “Periodicheskie svoistva mnogomernogo polinomialnogo generatora nad koltsom Galua. I”, Matem. vopr. kriptogr., 9:3 (2018), 61–98  mathnet  crossref  elib
    3. D. M. Ermilov, “Kolichestvo polinomialnykh preobrazovanii maksimalnogo perioda nad koltsami Galua nechetnoi kharakteristiki”, Matem. vopr. kriptogr., 9:4 (2018), 85–100  mathnet  crossref  elib
    4. V. E. Viktorenkov, “Tsiklovaya struktura sluchainykh podstanovok na mnozhestve dvukhtsvetnykh elementov. I”, Matem. vopr. kriptogr., 10:3 (2019), 9–32  mathnet  crossref
    5. O. A. Kozlitin, “Generatory psevdosluchainykh posledovatelnostei, ispolzuyuschie registrovye preobrazovaniya konechnykh tsepnykh kolets”, Matem. vopr. kriptogr., 10:3 (2019), 49–65  mathnet  crossref
  • Дискретная математика
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